Thực hiện phép tính:

a) \(2{x^2}{y^2}\left( {{x^3}{y^2} - {x^2}{y^3} - \frac{1}{2}{y^5}} \right)\)

\[ = 2{x^2}{y^2}\,.\,{x^3}{y^2} + 2{x^2}{y^2}\,.\,\left( { - {x^2}{y^3}} \right) + 2{x^2}{y^2}\,.\,\left( {\frac{{ - 1}}{2}{y^5}} \right)\]

\( = 2{x^5}{y^4} - 2{x^4}{y^5} - {x^2}{y^7}\).

b) \((x + y)\left( {{x^2}y - x} \right)\)

\( = x\,.\,{x^2}y + x\,.\,( - x) + y\,.\,{x^2}y + y\,.\,( - x)\)

\( = {x^3}y - {x^2} + {x^2}{y^2} - xy\).

c) \(\left( {2{x^3}{y^4}{z^2} - 3{x^4}{y^4}{z^3}} \right):\left( {\frac{{ - 1}}{3}x{y^3}z} \right)\)

\( = \left[ {\left( {2{x^3}{y^4}{z^2}} \right):\left( {\frac{{ - 1}}{3}x{y^3}z} \right)} \right] - \left[ {\left( {3{x^4}{y^4}{z^3}} \right):\left( {\frac{{ - 1}}{3}x{y^3}z} \right)} \right]\)

\( =  - 6{x^2}yz + 9{x^3}y{z^2}\).